One thing you may not be used to re: sound quality is the big improvement overall. Once you go hi-fi, even portable, it takes a while to realize what makes it truly hi-fi. At first, it just sounds like too much going on in your head, lol. Tendencies when you are starting out are to focus on how much louder or bassier things are, but as you grow to appreciate clarity, focus, detail, resolution, etc. etc. you can really begin to discern differences.
That said, a couple of answers for you:
Interconnects ARE really expensive, because they are aimed at us audio-junkies that feel like a $1000 cable is going to be an X% improvement over our "cheap" $100 ones. Chances are, unless you have an insanely revealing system, you're not going to gain a whole lot of improvement overall, and should be pretty much your last purchase concern for your system, or a "tweak" of your sound...
DAP - digital audio player. Used because "mp3 player" doesn't cover all file formats, and becaue people like acronyms, lol.
Portable amps - not always necessary, but they DO give an improvement overall. You'll find it more or less important, depending on the headphone in question. If they phones have a low impedance, you can get by driving them from the headphone jack. Some do cool things like the HeadRoom Total AirHead and the Meier Corda 2Move - they have crossfeed, which helps with ear fatigue, and gives a wider impression to the soundstage. Amps can also tighten up focus and drive the phones with more authority (better bass and treble response, for example - maybe not "more", but more focused).
EQ - by all means, fiddle with your settings, and see if you like they way they sound. I personally DON'T use the EQ, because with my Etymotics I prefer as neutral a sound as possible, and to me, the EQ can jsut give false impressions, but if your rig sounds to bassy, turn down the lower freqs, or add some treble. If they sound to bright, tinny, whatever, turn down some high end, and give them some bass, etc.